An alternate stable midpoint quadrature to improve the element stiffness matrix of quadrilaterals for application of functionally graded materials (FGM). (1st January 2017)

• Record Type: Journal Article
• Authors: Jeyakarthikeyan, P.V.; Subramanian, G.; Yogeshwaran, R.
• Is Part Of: Computers & structures. Volume 178(2016)
• Page Start: 71
• Page End: 87
• Publication Date: 2017-01-01
• Subjects: Quadrilateral element -- Stiffness matrices -- FGM -- Richardson extrapolation -- Hourglass instability -- Patch test -- Error estimation; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2016.10.008
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: A weighted integration route with robust stable one-point integration is recommended. It's an alternative to Gauss quadrature to obtain stiffness matrix of quadrilaterals. A weighted addition of the two approximations produces a far better stiffness matrix. Due to many simple sampling points, the method is most suited for FGM applications. Abstract: An efficient, stable and accurate quadrilateral element and its improved stiffness matrix on the midpoint quadrature concept is proposed in this research study. As a first approximation, the integrating point is considered as midpoint of the element of the mapped 2-square in the (ξ, η) plane (same as one-point Gauss-Quadrature). As a second approximation or stabilizing function, integrating points are assumed to be either at the midpoint of the four quadrants or four element edges of the mapped 2-square element in the (ξ, η) plane and these interpolated data are assembled. An appropriate weighted addition of the two approximations is found to result in a better and stable stiffness matrix than equivalent time delayed value of Gauss Quadrature.